Fuzzy multivariate mean square error in equispaced pareto frontiers considering manufacturing process optimization problems

Abstract

This paper proposes a combined approach using the normal boundary intersection (NBI) and multivariate mean square error (MMSE) that is an alternative approach to outperform the traditional NBI driving to an equispaced Pareto Frontier in a low-dimension space with a considerable reduction in the number of iterations. The method participating in the evolutionary stage of creating a uniformly spread Pareto Frontier for a nonlinear multi-objective problem is the NBI using normalized objective functions allied to MMSE. In sequence, the fuzzy MMSE approach is utilized to determine the optimal point of the multi-objective optimization. For sake of comparison, the performance of arc homotopy length, global criterion method, and weighted sums were explored. To illustrate this proposal, a multivariate case of AISI H13 hardened steel-turning process is used. Experimental results indicate that the solution found by NBI-MMSE approach is a more appropriate Pareto frontier that surpassed all the competitors and also provides the best-compromised solution to set the machine input parameters. Further, this algorithm was also tested in benchmark functions to confirm the NBI-MMSE efficiency.